As a young man, Menken enrolled in a premedical program at New York University but ultimately graduated with a degree in music. He then earned money by performing in clubs, composing advertising jingles, and providing accompaniment for ballerinas at practice. A career break came when playwright and lyricist Howard Ashman picked Menken to collaborate with him on the 1979 play God Bless You, Mr. Rosewater, based on a novel by Kurt Vonnegut. Although they attained mild success with that production, it was not until 1982 that they achieved significant critical and commercial acclaim with the Off-Broadway production of Little Shop of Horrors. The duo subsequently adapted their score for the 1986 film.

Ashman died in 1991 after having begun work with Menken on what would become another Disney success, Aladdin (1992), and Menken subsequently teamed up with lyricist Tim Rice. Aladdin became one of Disney’s biggest animated hits. Newsies (1992), a live-action Disney musical for which Menken wrote songs (with lyricist Jack Feldman), was less successful. For his next two Disney films, Menken collaborated with lyricist Stephen Schwartz on Pocahontas (1995) and The Hunchback of Notre Dame (1996). Pocahontas won Menken his seventh and eighth Academy Awards, in the categories of best musical or comedy score and best original song (“Colors of the Wind”). Menken later worked with David Zippel on the score for Hercules (1997) and again with Schwartz on the music for Enchanted (2007). Other films for which he contributed scores include Tangled (2010; with lyricist Glenn Slater) and Mirror Mirror (2012; Menken wrote lyrics for all but one song).

Menken also continued to work in the theatre. With Slater he composed for the musicals Sister Act (first performed 2006) and Leap of Faith (2010), both of which were based on 1992 films. He made stage adaptations of Beauty and the Beast (1994), The Little Mermaid (2008), Newsies (2012), and Aladdin (2014). Though Newsies was not a huge hit on-screen, the stage production earned Menken a Tony Award for best original score.